Jingfei bought a house 5 years ago for $350,000. Her down payment on the house was the minimum required 10% at that time she financed the remainder with a 15-year fixed rate mortgage. The annual interest rate was 9% and she was required to make monthly payments, and she has just made her 60th payment. A new bank has offered to refinance the remaining balance on Jingfei's loan and she will have to pay $3,230 per month for the next 10 years, but the total fees she will have to pay today to get the new loan is $1,000. Should she take the new offer? How much will she gain or lose in today's dollars if she does? Annual interest rates are still 9%.
First of all, I will assume that the 9% was compounded monthly, or else
our standard formulas are not valid, so
i = .09/12 = 0075
actual mortgage = .90(350000) = 315000
n = 15*12 = 180
payment = p
p(1 - 1.0075^-180 )/.0075 = 315000
p = 3,194.94 <---- original monthly payment
So this done for 60 payments
Outstanding balance after 60 payments of this
= 315000(1.0075)^60 - 3194.94(1.0075^60 - 1)/.0075
= 252,213.93
cost of new plan = 1000
so new mortgage = 253,213.93
n = 120
i = still .0075
newpayment = np
np(1 - 1.0075^-120)/.0075 = 253213.93
np = 3207.61
So, what is your conclusion ?
remember if she does not take it, the payment stays at $3,194.94
Looks like a no brainer to me
To determine whether Jingfei should take the new offer to refinance her loan, we need to compare the remaining cost of her current loan with the cost of the new loan, taking into account the fees she will have to pay today.
First, let's calculate the remaining balance on Jingfei's current loan after 60 payments. Since she has a 15-year fixed-rate mortgage and has just made her 60th payment, she has made 5 years' worth of monthly payments.
The remaining balance on her current loan can be calculated using the amortization formula:
Remaining Balance = Principal * [(1 + Monthly Interest Rate) ^ Total Payments] - [(1 + Monthly Interest Rate) ^ Total Payments - 1] / Monthly Interest Rate
Principal = Original Loan Amount - Down Payment
Monthly Interest Rate = Annual Interest Rate / 12
Total Payments = Remaining Loan Term in months - Number of Payments Made
Principal = $350,000 - ($350,000 * 10%) = $350,000 - $35,000 = $315,000
Monthly Interest Rate = 9% / 12 = 0.75%
Total Payments = 15 years * 12 months/year - 60 months = 180 months - 60 months = 120 months
Now we can calculate the remaining balance:
Remaining Balance = $315,000 * [(1 + 0.0075) ^ 120] - [(1 + 0.0075) ^ 120 - 1] / 0.0075
Remaining Balance = $223,468.13
Next, let's calculate the total cost of the new loan if Jingfei decides to refinance.
Total Cost of New Loan = Monthly Payment * Number of Payments + Fees
Monthly Payment = $3,230
Number of Payments = 10 years * 12 months/year = 120 months
Fees = $1,000
Total Cost of New Loan = $3,230 * 120 + $1,000 = $387,600 + $1,000 = $388,600
To determine whether Jingfei should take the new offer, compare the remaining balance on the current loan ($223,468.13) with the total cost of the new loan ($388,600). If the remaining balance is lower, it is more cost-effective for Jingfei to continue with her current loan. If the total cost of the new loan is lower, Jingfei should consider refinancing.
In this case, the total cost of the new loan ($388,600) is higher than the remaining balance on her current loan ($223,468.13). Therefore, it is not financially advantageous for Jingfei to refinance her loan.
To determine how much Jingfei will gain or lose in today's dollars, we can calculate the difference between the remaining balance on her current loan and the total cost of the new loan:
Difference = Total Cost of New Loan - Remaining Balance
Difference = $388,600 - $223,468.13 = $165,131.87
Therefore, if Jingfei decides to take the new offer, she will lose $165,131.87 in today's dollars compared to continuing with her current loan.